Contemporary Abstract Algebra: Textbooks in Mathematics
Autor Joseph Gallianen Limba Engleză Hardback – 10 feb 2025
For more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.
The author presents the concepts and methodologies of used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do.
This new edition is streamlined. The 10th edition had 26 new examples, 330 new exercises, a few new theorems, and a substantial, number of minor modifications to the explanatory material, discussion text, and proofs. We have omitted suggested readings, references, biographies, etc that tally to 56 pages less. A number of corrections were also made for this edition.
Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The hallmark features of previous editions of the book are enhanced in this edition. These include:
- A good mixture of approximately 1900 exercises.
- Approximately 300 worked-out examples
- Many applications from scientific and computing fields and everyday life.
- Historical notes and biographies that spotlight people and events.
- Motivational and humorous quotations.
- Numerous connections to number theory and geometry.
While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual offers solutions for all the exercises. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises and is well-loved for alternative solutions as well.
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Specificații
ISBN-13: 9781032778914
ISBN-10: 1032778911
Pagini: 556
Ilustrații: 144
Dimensiuni: 156 x 234 mm
Ediția:11
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics
Locul publicării:Boca Raton, United States
ISBN-10: 1032778911
Pagini: 556
Ilustrații: 144
Dimensiuni: 156 x 234 mm
Ediția:11
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics
Locul publicării:Boca Raton, United States
Public țintă
Undergraduate AdvancedCuprins
1 Introduction to Groups2 Groups3 Finite Groups; Subgroups4 Cyclic Groups5 Permutation Groups6 Ismorphisms7 Cosets and Lagrange's Theorem8 External Direct Products9 Normal Subgroups and Factor Groups10 Group Homomorphisms11 Fundamental Theorem of Finite Abelian Groups12 Introduction to Rings13 Integral Domains14 Ideals and Factor Rings15 Ring Homomorphisms16 Polynomial Rings17 Factorization of Polynomials18 Divisibilty in Integral Domains19 Extension Fields20 Algebraic Extensions21 Finite Fields22 Geometric Constructions23 Sylow Theorems24 Finite Simple Groups25 Generators and Relations26 Symmetry Groups27 Symmetry and Counting28 Cayley Digraphs of Groups29 Introduction to Algebraic Coding Theory30 An Introduction to Galois Theory31 Cyclotomic Extensions
Notă biografică
Joseph A. Gallian earned his Ph.D. from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.
Descriere
CONTEMPORARY ABSTRACT ALGEBRA, 11e stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists